Full text: Bernoulli, Daniel: Hydrodynamica s. de viribus et motibus fluidorum commentarii

HYDRODYNAMICÆ (M X {Nv/M} + ndx X o): (M + ndx) = {Nv/M + ndx}. Poſtquam vero particula
n d x ſuperne jam affuſa eſt, communem acquiſivit motum cum aqua proxi-
me inferiori, ſicque fit aſcenſus potentialis ejusdem aquæ in ſitu c d m l o n p i c
æqualis tertiæ proportionali ad ſpatium C D L O N P I C (M + ndx), ſpa-
tium D t u x y O L D (N + ndx) & altitudinem v + dv, id eſt, =
{(N + ndx) x (v + dv)/M + ndx}, cujus exceſſus ſupra priorem aſcenſum potentialem eſt =
{Ndv + nvdx + ndxdv/M + dx} =, rejectis differentialibus ſecundi ordinis, {Ndv + nvdx/M}. Habetur igitur talis æquatio {Ndv + nvdx/M} = {nadx/M}, quæ ut prior per tra-
ctata & ad finem deducta dat
x = {N/n} log. {a/a - v}, vel
v = a X (1 - c {-nx/N})
quæ ſolutio valet pro affuſione laterali.

73. Scholion 1.

§. 4. Sunt hæ æquationes inter ſe admodum diverſæ; diverſitas au-
tem eo major quo minoris eſt amplitudinis vas; & ſi quidem amplitudo va-
ſis ſuprema in cd quaſi infinita ſit præ amplitudine foraminis, evaneſcit n
præ m fitque in priori caſu ſicut in poſteriori. v = a X (1 - c {-n/N}x )
Eſt igitur hâc in hypotheſi motus utrobique idem quod haud difficulter
quisque prævidere potuerit. Celerior autem ſemper eſt cæteris paribus mo-
tus in priori affuſione, quam in altera.

Conveniet hic rem etiam phyſice explicare, ut eam diſtinctius in omni-
bus phænomenis percipere poſſimus.

Sit loco vaſis cujuſcunque & quamcunque directionem habentis bre-
vioris delineationis gratia cylindrus verticalis cum foramine in fundo, nempe
G H N D (Fig. 29.) ſitque dein vas E F P Q perforatum in R S; fingantur orifi-
cia RS & GD perfecte æqualia, & ad minimam diſtantiam ſibi perfecte re-

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer